Statistics and Probability Answers

A lawyer claims that the average years of settling criminal cases filed before courts is three

and a half years. To test the claim, a watchdog organization randomly selected 35 criminal

cases and recorded the years the cases took before the courts have been rendered verdicts.

The sample mean was 4 years with a standard deviation of three and a half years. Do the

data gathered by the said organization provide sufficient basis to accept the claim of the

lawyer? Use 0.05 level of significance.

A company claimed that their N95 face mask has a mean filtration efficiency rate of

95%. A group of student researcher wanted to verify this claim. They bought and tested

40 of their N95 face masks. They found out that the average filtration efficiency rate of

these face mask was 90% with a standard deviation of 4%. Test the claim at 5% level

of significance and assume that the population is approximately normally distributed.

A survey unofficially claimed that in every five young executives, only one practices good reading habits.

a. What is the probability that out of 10 young executives, two executives practice good reading habits?

b. What is the probability that at least five out of 20 young executives practice good reading habits?

the following data were obtained by sampling a population

5

3

7

5

6

8

6

5

9

Compute for the mean.

A population has mean 75 and standard deviation 12.

a.)Random samples of size 121 are taken. Find the mean and standard deviation of sampling distribution of the means?

b.)How would the answers to part (a) change if the size of the samples were 400 instead of 121?

find the class boundaries, midpoint, and width for the class 12.4-15.2

State whether the following statement true or false

QUESTION 4

The number of arrivals per minute at a bank located in the central business district of a large city

was recorded over a period of 200 minutes, with the following results:

Arrivals Frequency

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

The probability of at least two arrivals per minute at the bank is 0:155:

QUESTION 26

A local fire station receives on average 8.5 emergency telephone calls per hour. Assume that

these calls are Poisson distributed. Calculate the probability that

(a) the fire station will get nine calls during one hour. (2)

(b) the fire station will get five to seven (inclusive) calls during one hour. (3)

(c) the fire station will get at least 4 calls during one hour. (3)

(d) the fire station will get more than 6 calls during one hour.

QUESTION 25

Suppose that X is a binomial random variable with n D 25 and p D 0:5: Calculate

(a) the probability P .X D 15/: (2)

(b) the probability P .X  16/: (4)

(c) the expected value of X. (2)

(d) the variance of X. (3)

QUESTION 24

According to a report from the research for Studying Health System Change, 20% of South Africans

delay or go without medical care because of concerns about cost. Suppose that 8 individuals are

randomly selected.

(a) What is the probability that two individuals will delay or go without medical care? (2)

(b) What is the probability that at most two individuals will delay or go without medical care? (3)

(c) What is the probability that at least seven individuals will delay or go without medical care?

(3)

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